The effect of the sector structure of the interplanetary magnetic field on the galactic cosmic ray anisotropy

M. V. Alania

Geophysical Institute, Tbilisi, Georgia

T. V. Bochorishvili and K. Iskra

Institute of Physics and Mathematics, Sedlse, Poland

Received December 15, 1999

Contents

Abstract

Introduction

The effect of the sector structure of the interplanetary magnetic field (IMF) on the galactic cosmic ray (GCR) anisotropy is of a great interest. On the one hand, it allows us to solve the problem of the effect of particle drift on the GCR anisotropy, which still remains important. On the other hand, when the effect of particle drift on the anisotropy is determined rather reliably, we can develop a set of algebraic equations involving the spatial components of the GCR anisotropy derived from experimental data. This set of equations may be consequently used to calculate the components of the tensor of the GCR anisotropic diffusion and the solar wind parameters. According to Alania et al. [1983, 1987] and Riker and Ahluwalia [1987], the set of equations for the GCR anisotropy components is

(1)

(2)

(3)

Here K_d, K_f, and K_| are the drift diffusion coefficient and cross-field and field-aligned (relative to the IMF lines) diffusion coefficients of GCR, respectively; G_r, G_q, and G_j are the radial, heliolatitudinal, and azimuth gradients of the GCR in the interplanetary space, y is the angle between the IMF lines and the Sun-Earth line, U and V are the velocities of the solar wind and GCR particles, respectively, and C is the Compton-Getting effect ( C 1.5 for the GCR particle energy detected by the neutron monitors). As (1)-(3) demonstrate, the GCR anisotropy (detected by the neutron monitors at the Earth's surface) is caused mainly by diffusion, convection, and drift of GCR particles in the regular IMF. On the average, it is 0.3-0.4%. Alania et al. [1983, 1987] have shown that in this case the particle drift contribution can amount to 15-20% of the mean anisotropy. We should distinguish two types of the drift effect on the GCR anisotropy. The first one caused by the gradient and curvature of the global IMF can be derived from the measurements of the mean diurnal GCR variation in different solar cycles, qA>0 and qA<0 (when qA>0, the IMF lines exit from the northern solar hemisphere, and when qA<0, they enter the northern solar hemisphere). The second drift type caused by the existence of local spatial gradients of the GCR manifests itself in different sectors of the IMF. However, whereas the drift of the first type can be derived from the GCR anisotropy merely by averaging the data over a long period (for instance, 11 years), it is difficult to unambiguously reveal the drift effect of the second type because of considerable variations in the solar wind parameters during short periods comparable with durations of the positive and negative sectors of the IMF.

Investigation Methods and Discussion

The goal of this paper is to reveal the effect of the drift of the second type on the GCR anisotropy in different positive and negative sectors of the IMF and to calculate the solar wind velocity, components of the anisotropic diffusion tensor, and other GCR modulation characteristics by using (1)-(3). The most important parameter is the K/K ratio (K/K = a). It demonstrates the character of variations in the IMF irregularity and determines the role of the GCR particle drift in the heliosphere. Alania et al. [1983] have analyzed the set of equations (1)-(3) assuming that the GCR gradients in the opposite IMF sectors are equal to each other. In order to determine the anisotropy components A_r and A_j, the method of harmonic analysis was applied. A similar work without specific calculations has been recently performed by Ahluwalia and Dorman [1997]. In this work the effect of the drift on the GCR anisotropy was deduced from the data for the period of the solar minimum in 1976. It is known that during the periods of solar minimum the IMF sector structure is rather pronounced. However, not only the short-period variations in the solar wind parameters and GCR intensity, but also the variations related with the Sun rotation period are weak [Alania et al., 1983; 1987]. Contrary to our previous papers, here we use the global survey method for determination of the A_r, A_q, and A_j spatial components of the GCR anisotropy [Belov et al., 1995]. Moreover, the calculations were performed for the positive and negative sectors no shorter than 4 days. The latter condition is a rigorous criterion for the data selection and reduces the amount of statistical material. However, in this case the effect of a certain sector of the IMF on particle travel can be revealed more reliably, that is, the GCR particle drift in the regular IMF can be determined relatively reliably. While averaging the data over a period much longer than the Sun rotation period, we may assume that the heliolongitudinal gradient is zero (G_j = 0). Taking into account that G_j = 0 and performing a simple transformation, we obtain, instead of (1)-(3), the following set of equations:

(4)

(5)

(6)

Here a and a₁ are the ratios between the cross-field K_f and drift K_d diffusion coefficients to the field-aligned diffusion coefficient K_|, respectively (K/K_| = a, K_d/K_| = a₁). Now the set of equations (4)-(6) takes the form:

(7)

(8)

(9)

(10)

(11)

(12)

where G_r⁺, G_r^-, G_q⁺, and G_q^- are the radial and heliolongitudinal gradients of GCR in different IMF sectors.

The anisotropy components A_r⁺, A_r^-, A_q⁺, A_q^-, A_j⁺, and A_j^- were found by using the data from the neutron monitors of the worldwide network of stations for the period of solar minimum (1976). The data for the IMF polarity were taken from Zaitsev [1984]. The neutron monitors (especially those with the cutoff thresholds lower than 5 GV) were selected taking into account similar characters of changes in the diurnal variation in different IMF sectors, which was determined by the ordinary harmonic analysis. Table 1 lists the stations of neutron monitors used in the global survey analysis. It also presents the number of days used for the analysis of data for different IMF sectors at each station. These periods are different because, for some stations, the changes in the diurnal variation amplitudes higher than 0.7% were not considered. Hourly data from each station were averaged, and thus the average diurnal waves for each IMF sector for 1976 were obtained. Then the GCR anisotropy components A_r⁺, A_r^-, A_q⁺, A_q^-, A_j⁺, and A_j^- were determined by the global survey method.

When using the obtained GCR anisotropy components A_r⁺, A_r^-, A_q⁺, A_q^-, A_j⁺, and A_j^- to solve (7)-(12), one should take into account that, whereas the components A_r⁺, A_r^-, A_j⁺, and A_j^- can be determined rather reliably, there is an uncertainty in the A_q⁺ and A_q^- components. This problem is connected with a possible north-south asymmetry of the GCR intensity and heliolatitudinal gradient. For a reliable determination of the northsouth asymmetry of the GCR intensity, special investigations using the solar activity data are required.

Therefore, only the A_r⁺, A_r^-, A_j⁺, and A_j^- components of the GCR anisotropy may be used when solving (7)-(12). However, in this case the number of unknowns exceeds the number of equations, and certain simplifications are required. Assume that the like GCR gradients in different IMF sectors equal each other, that is, G_r⁺ = G_r^- and G_q⁺ = G_q^-. In addition, we may also use equation (10) under the assumption that there is a north-south asymmetry of GCR which remains constant during a year, for instance, 1976. Then the set of equations (7)-(12) looks like

(13)

(14)

(15)

(16)

(17)

The global survey with the use of the data from the worldwide network of neutron monitors gave the following results: A_r⁺ = -0.20%, A_r^- = -0.11%, A_j⁺ = -0.28%, and A_j^- =-0.19%. Using (13) and (16) and the equation Ref. 4/A [Parker, 1965] (where W is the angular velocity of the Sun and R₀ is the Sun-Earth distance), we have estimated the angle between the IMF lines and the Sun-Earth line to be y 46^o, and the solar wind velocity was found to be U 420 km s^-1. This value is in good agreement with the average solar wind velocity at the Earth's orbit, U 450 km s^-1, obtained by direct measurements in the interplanetary space [King, 1979]. Using the obtained y and U and equations (14) and (15), we have calculated a = K/K 0.33 0.05 (the ratio between the cross-field and field-aligned diffusion coefficients of GCR). This value is 4-5 times higher than a = 0.05-0.1 taken by various authors in numerical solution of the equation for the GCR anisotropic diffusion. The overestimation is possibly due to the assumption that the spatial gradients in different IMF sectors are equal, that is, G_r⁺ = G_r^- and G_q⁺ = G_q^-. We have also calculated the ratio between the drift diffusion coefficient K_d and the field-aligned diffusion coefficient K_| a₁ 0.47 0.05, the product of the field-aligned diffusion coefficient by the radial GCR gradient K_| G_r = 7.2 10⁹ cm^-1 % AU^-1, and the product of the field-aligned diffusion coefficient by the heliolatitudinal gradient of GCR K_| G_q= 1.4 10⁹ cm ² s^-1 % AU^-1 (AU is the astronomic unit). If we assume the average radial gradient to be 2% per AU, %%% ??? then K = 3.6 10²² cm² s^-1 and the heliolatitudinal gradient is G_q = 0.4% per AU. %%% ??? Unfortunately, the set of equations (8)-(12) cannot be solved for G_r⁺, G_r^-, G_q⁺, and G_q^- because of the lack of information on absolute values of the anisotropy components A_q⁺ and A_q^- due to uncertainty of the north-south asymmetry of GCR intensity.

Conclusions

(1) Using the data from the global network of neutron monitors and the global survey method, we have unambiguously determined the effect of particle drift (  0.04-0.05%) on both the azimuth and radial components of the GCR anisotropy at the solar minimum (1976). The magnitude of the GCR anisotropy vector in the positive IMF sector is higher, and the phase is shifted toward earlier hours.

(2) Solving the set of algebraic equations derived by using the GCR anisotropy spatial components for 1976, we have determined the following quantities: the angle between the IMF lines and the Sun-Earth line y 46^o ; the solar wind velocity U 420 km s^-1 (direct measurements in the interplanetary space give the mean solar wind velocity at the Earth's orbit equal to 450 km s^-1 ); the ratio between the cross-field K and field-aligned K GCR diffusion coefficients a 0.33 0.05 ; the ratio between the drift K_d and field-aligned K_| diffusion coefficients a₁ 0.47 0.05.

Acknowledgments

References

Ahluwalia, H. S., and L. I. Dorman, Computation of transverse cosmic ray particle density gradients, in Proceedings of the 25th International Cosmic Ray Conference, vol. 2, pp. 101-104, Durban, South Africa, 1997.

Alania, M. V., et al., The effect of the particle drift on cosmic ray anisotropy, in Proceedings of the 18th International Cosmic Ray Conference, vol. 10, pp. 91-94, Bangalore, India, 1983.

Alania, M. V., et al., Modulation of Galactic Cosmic Rays by the Solar Wind, edited by M. Kats, pp. 3-94, Metsniereba, Tbilisi, 1987 (in Russian).

Belov, A. V., E. A. Eroshenko, K. F. Yudakhin, and V. G. Yanke, Isotropic and anisotropic variations in cosmic rays in March-June, 1991, Izv. Akad. Nauk Ross. Ser. Fiz., 59 (4), 79, 1995 (in Russian).

King, J. H., Interplanetary Medium Data Book, Suppl. 1, World Data Center A, Greenbelt, Maryland, 1979.

Parker, E. N., The passage of energetic charged particles through interplanetary space, Planet. Space Sci., 13, 9, 1965.

Riker, J. F., and H. S. Ahluwalia, A survey of the cosmic ray diurnal variation during 1973-1979, II,  Application of diffusion-convection model to diurnal anisotropy data, Space Sci., 35, 9, 1117, 1987.

Zaitsev, A. R., The interplanetary magnetic field polarity during 1957-1989. Mansurov's Catalogue, preprint 52 (526), IZMIRAN, 1984 (in Russian).